대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제55권2호
  • /
  • Pages.331-340
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  • 2018
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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SCALAR CURVATURE COMPARISONS OF LEVEL HYPERSURFACES OF GEODESIC SPHERES

  • Kim, Jong Ryul (Department of Mathematics Kunsan National University)
  • 투고 : 2016.07.16
  • 심사 : 2018.02.27
  • 발행 : 2018.03.31
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초록

Using the comparison of differential equations involving Ricci and scalar curvatures obtained by Eschenburg and O'Sullivan, the scalar curvatures of level hypersurfaces of geodesic spheres are compared.

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참고문헌

  1. R. Bishop, A relation between volume, mean curvature and diameter, Notices Amer. Math. Soc. 10 (1963), 364.
  2. R. L. Bishop and R. J. Crittenden, Geometry of Manifolds, Pure and Applied Mathematics, Vol. XV, Academic Press, New York, 1964.
  3. J. Cheeger and T. H. Colding, On the structure of spaces with Ricci curvature bounded below. I, J. Differential Geom. 46 (1997), no. 3, 406-480. https://doi.org/10.4310/jdg/1214459974
  4. P. E. Ehrlich, Y.-T. Jung, and S.-B. Kim, Volume comparison theorems for Lorentzian manifolds, Geom. Dedicata 73 (1998), no. 1, 39-56. https://doi.org/10.1023/A:1005096913126
  5. P. E. Ehrlich and M. Sanchez, Some semi-Riemannian volume comparison theorems, Tohoku Math. J. (2) 52 (2000), no. 3, 331-348. https://doi.org/10.2748/tmj/1178207817
  6. J.-H. Eschenburg and E. Heintze, Comparison theory for Riccati equations, Manuscripta Math. 68 (1990), no. 2, 209-214. https://doi.org/10.1007/BF02568760
  7. J.-H. Eschenburg and J. J. O'Sullivan, Jacobi tensors and Ricci curvature, Math. Ann. 252 (1980), no. 1, 1-26. https://doi.org/10.1007/BF01420210
  8. J. R. Kim, Comparisons of the Lorentzian volumes between level hypersurfaces, J. Geom. Phys. 59 (2009), no. 7, 1073-1078. https://doi.org/10.1016/j.geomphys.2009.04.011
  9. J. R. Kim, Relative Lorentzian volume comparison with integral Ricci and scalar curvature bound, J. Geom. Phys. 61 (2011), no. 6, 1061-1069. https://doi.org/10.1016/j.geomphys.2011.02.005
  10. D. N. Kupeli, On conjugate and focal points in semi-Riemannian geometry, Math. Z. 198 (1988), no. 4, 569-589. https://doi.org/10.1007/BF01162874